Perceptual decisions requiring the comparison of spatially distributed stimuli that are fixated sequentially might be influenced by fluctuations in visual attention. We used two psychophysical tasks with human subjects to investigate the extent to which visual attention influences simple perceptual choices, and to test the extent to which the attentional Drift Diffusion Model (aDDM) provides a good computational description of how attention affects the underlying decision processes. We find evidence for sizable attentional choice biases and that the aDDM provides a reasonable quantitative description of the relationship between fluctuations in visual attention, choices and reaction times. We also find that exogenous manipulations of attention induce choice biases consistent with the predictions of the model.